Re: Vignetting due to lens or sensor?

In article <qcKdncQn5dxRMKfXnZ2dnUVZ_vOdnZ2d@xxxxxxxxxxxx>, Alan Browne <alan.browne@xxxxxxxxxxxxxxxxxxxxx> writes
On 18-06-09 17:01, Jim wrote:
The reduction of light in the corners is actually the fourth power of the
cosine of the angle of incidence of the light.
Jim

As I said in another post would you please back that up.

There are 3 steps to this, as follows:
1. The apparent area of the focal plane is proportional to the cosine of the angle of incidence. eg. a flat piece of paper has area AxB when viewed perpendicularly, but has apparent area Ax0 when viewed at grazing angle from side A. The angle between perpendicular and grazing is 90deg, and cos(90)=0.

So the number of photons incident on the focal plane is proportional to the cosine of their angle of incidence.

2. The apparent size of the lens aperture is proportional to the cosine of the angle - for the same reasons as 1.

3. The distance from the centre of the lens to any point on the focal plane is inversely proportional to the cosine of the angle, and the intensity of image is inversely proportional to the square of the distance. ie. the intensity of the image is proportional to cos^2.

Multiply these three terms up and you get the well known, but vastly overgeneralised, cos^4 law.

In most photographic lenses the rays which form the image at any part of the focal plane do not originate from all of the rear element of the lens, and this leads to a significant departure from the cos^4 law. The rays from, say, the central 20% area of the rear element may form the central part of the image, while the rays from a similar 20% area closer to the edge of the rear element may form the image in the appropriate corner. This is particularly true of wide angle retrofocus and telecentric lens designs. As a consequence of this, the angle of incidence in the corners is not the same as the angle from the corner to the centre of the rear element, and hence the "cos^4" law fails in terms of using the field size and focal length.

In detail it still holds true for each element of the lens area which contributes photons to each part of the image, but that requires much more computation than a simple "cos^4".
--
Kennedy
Yes, Socrates himself is particularly missed;
A lovely little thinker, but a bugger when he's pissed.
Python Philosophers (replace 'nospam' with 'kennedym' when replying)
.

Relevant Pages

  • Re: Solar panel energ vs. incidence angle?
    ... but basically the reflectance of a surface is ... approximately proportional to the cosine of the angle of incidence. ...
    (sci.physics)
  • Re: Solar panel energ vs. incidence angle?
    ... but basically the reflectance of a surface is ... approximately proportional to the cosine of the angle of incidence. ...
    (sci.energy)
  • Re: Light fall off on dSLRs - an experiment
    ... incidence on a dSLR then propose it. ... element closest to the sensor.. ... and suitable wide angle, I can't do that. ... from various areas of the lens will actually *hit* the sensor from ...
    (rec.photo.digital.slr-systems)
  • Re: Light fall off on dSLRs - an experiment
    ... By placing the source far away from the focal plane that effect is minimised so that the angle of incidence is the same for *all* pixels in the frame and controlled simply by rotating the camera relative to the point source. ... light fall off due to incident angle to the sensor would still have ... I was trying to measure the alleged variation in sensitivity of digital sensors to angle of incidence of, not distance from, the light source! ...
    (rec.photo.digital.slr-systems)
  • Re: how to get the angle from the cosine, etc.
    ... >that you already have the sine and cosine of the angle. ... What we are forced to do is to _define_ the inverse cosine as a new ... If you also know the sine, then you have a unique solution within ...
    (sci.math)